SPIRALS IN POTENTIAL VORTICITY - PART-I - MEASURES OF STRUCTURE

Advection in weather systems results in filamentary and spiral structu res in tracers, whose complexity increases as stirring progresses. Cha racterizations of fine-scale structures in chemical tracers, which are typically unresolved in atmospheric analyses or models, may enable a treatment of mixing between air masses that is very different from a s imple diffusion. In addition, filaments in Ertel potential vorticity ( PV) and other active tracers can have a direct influence on the surrou nding flow that will depend to some extent upon their spatial arrangem ent as well as internal structure. Here attention is focused on a part icular baroclinic wave life cycle that is distinguished by the existen ce of an exceptionally persistent, synopfic-scale, cyclonic vortex. In this region the PV field exhibits a spiral-shaped filament that is ev entually disrupted by vortex rollup due to the nonlinear development o f barotropic instability. Similar spirals have been observed in satell ite imagery. In this paper the characterization of the structure of PV spirals by a geometrical measure and by a spectral measure and the re lationship between the two is considered. The scale-invariant nature o f a spiral can be characterized geometrically by the Kolmogorov capaci ty (or box-counting dimension) of the set of points of intersection be tween the spiral and a cut through it (D'(K)). The capacity of the spi ral in the baroclinic wave is found to be almost constant (D'(K) appro ximate to 0.4) during a period when the number of turns increases from 2 to 5. The constancy of D'(K) results from the:steadiness of the red ial dependence of angular velocity. Another, more traditional, measure of tracer structure is the power spectrum, which might be expected to be related to Kolmogorov capacity in the scale-invariant subrange. Ho wever, total wavenumber spectra for PV in the life cycle show two subr anges with very different spectral slopes, neither of which relate to the value of capacity. It is hypothesized that the observed atmospheri c kinetic energy spectrum is also not directly related to accumulating discontinuities in PV because the scale-invariant subrange of PV stru ctures, from synoptic scales to mesoscales, is too narrow. In conclusi on, the Kolmogorov capacity is a more useful measure of structures for med by advection. For instance, the capacity of PV spirals is used as the basis for an investigation of their stability in Part II. The char acterization of tracer structure with geometrically based measures, li ke Kolmogorov capacity, could also be helpful in studies of mixing.